The four number game

The Four Numbers Game is a mathematical game, as taught by Dr. Paul Sally, Prof. of Mathematics at the University of Chicago. To play this game, draw a square and put a number at each corner, thus:

5___9
|   |
|   |
|   |
7___13
      

Now form a new square based on the difference between each the values at the ends of each side. Example:

5_4_9
|   |
2   4
|   |
7_6_13
      

This gives a new square, which I'll rotate anticlockwise 45 degrees.

4___4
|   |
|   |
|   |
2___6
      

This in turn gives

0___2
|   |
|   |
|   |
2___4
      

Then

2___2
|   |
|   |
|   |
2___2
      

Then

0___0
|   |
|   |
|   |
0___0
      

At this point, the game is over.

Codes for geting any four given numbers:

1. Sub FourNumbers(ByRef steps As String, ByRef count As Long, ParamArray s())
2. Dim temp As String, tempcount As Long
3. count = 1
4. If s(0) & s(1) & s(2) & s(3) = "0000" Then steps = Join(s, ","): Exit Sub
5. FourNumbers temp, tempcount, Abs(s(0) - s(1)), Abs(s(1) - s(2)), Abs(s(2) - s(3)), Abs(s(3) - s(0))
6. steps = Join(s, ",") & vbCrLf & temp
7. count = tempcount + 1
8. End Sub
9. Sub Getit()
10. Dim steps As String, count As Long
11. FourNumbers steps, count, [exp(1)], [pi()], 1, 0
12. Debug.Print "Count=" & count & vbCrLf & String(50, "-") & vbCrLf & steps
13. FourNumbers steps, count, 149, 274, 504, 927
14. Debug.Print "Count=" & count & vbCrLf & String(50, "-") & vbCrLf & steps
15. End Sub

It returns:

Count=5

--------------------------------------------------

2.71828182845905,3.14159265358979,1,0

0.423310825130748,2.14159265358979,1,2.71828182845905

1.71828182845905,1.14159265358979,1.71828182845905,2.2949710033283

0.576689174869252,0.576689174869252,0.576689174869252,0.576689174869252

0,0,0,0

Count=19

--------------------------------------------------

149,274,504,927

125,230,423,778

105,193,355,653

88,162,298,548

74,136,250,460

62,114,210,386

52,96,176,324

44,80,148,272

36,68,124,228

32,56,104,192

24,48,88,160

24,40,72,136

16,32,64,112

16,32,48,96

16,16,48,80

0,32,32,64

32,0,32,64

32,32,32,32

0,0,0,0